Someone with authority to act is a person that your business has granted permission to act on your behalf.
This is usually with Inland Revenue or with your bank, and would include people such as an administrator or general manager who is allowed to access business tax data, or office staff who have been permitted to view bank records and make payments (for example).
If you have someone that is not a director, shareholder, trustee, etc, who can make significant legally binding decisions on behalf of the business, then they probably have authority to act.